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Steven’s Law

A law relating the objective, instrument-measured intensity of a stimulus to its intensity as perceived by a human, enunciated by Stanley S. Stevens (1906 – 1972) in 1957. It addresses the same question that Fechner did almost 100 years earlier, but while Fechner postulated that the perceived intensity is always related logarithmically to the physical intensity, Steven's law says the magnitude of the perceived intensity is related to the magnitude of the physical intensity raised to some power. It is sometimes simply called the Power Law.

where Ψ is the perceived intensity, Φ is a measure of the physical intensity, and k and n are constants. One of Steven's main contributions was showing that n varies according to the nature of the stimulus. Some examples of n:

values of n for various stimuli
Stimulus	n
brightness of light	0.3
saccharin	0.8
saltiness	1
sucrose	1.5 (showing that its sweetness is not sensed in the same manner as saccharin’s)
temperature	1.6
electric shock	3.5

S. S. Stevens.
On the psychophysical law.
Psychological Review, vol 64, number 3, pages 153-81. (May 1957)

resources

A nice interactive presentation by John H. Krantz of Steven's Law is
isle.hanover.edu/Ch02Methods/Ch02PowerLaw_evt.html